Vol

A personal learning project on volatility, smile, surface, etc.

Stochastic Volatility Inspired (SVI)

The SVI parameterization of the implied volatility smile was originally devised at Merrill Lynch in 1999 by Jim Gatheral.

k: log-moneyness = ln(K/F)

w: total variance = IV^2 * T

Parameters:

• a: vertical shift (general variance)
• b: slope (tightness of smile)
• ρ: skew
• m: horizontal shift
• σ: ATM curvature

Interactive Plot

To "feel" the SVI and its parameters, I created an intractive plot at ghasimi.github.io/vol